Abstract: Determining the global stability of a pressurized water reactor (PWR) core nonlinear system is the problem to be solved. In the paper, the core nonlinear system was modeled and the linearized model of the system was obtained via the small perturbation method. According to the distributing situation of the core nonlinearity measure in the power level range based on the equilibrium manifold, seven linear models corresponding to seven power levels respectively were chosen as local models of the core and the set of seven local models was used to approximately substitute the core system. The global stability of the PWR core nonlinear system was analyzed by utilizing Lyapunov stability theory. The calculated result shows that the core nonlinear system is globally and asymptotically stable. The modeling method of the core is effective in analyzing the global stability of a PWR core nonlinear system.